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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Continuity of the maximal operator in Sobolev spaces


Author: Hannes Luiro
Journal: Proc. Amer. Math. Soc. 135 (2007), 243-251
MSC (2000): Primary 42B25, 46E35, 47H99
Published electronically: June 30, 2006
MathSciNet review: 2280193
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Abstract: We establish the continuity of the Hardy-Littlewood maximal operator on Sobolev spaces $ W^{1,p}(\mathbb{R}^n)\,$, $ 1<p<\infty\,$. As an auxiliary tool we prove an explicit formula for the derivative of the maximal function.


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Additional Information

Hannes Luiro
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), 40014 University of Jyväskylä, Finland
Email: haluiro@maths.jyu.fi

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08455-3
PII: S 0002-9939(06)08455-3
Keywords: Maximal function, Sobolev spaces, continuity, regularity
Received by editor(s): June 4, 2004
Received by editor(s) in revised form: August 8, 2005
Published electronically: June 30, 2006
Additional Notes: The author was supported by the Academy of Finland, project 201015
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.